GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 23 Sep 2018, 18:58

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

If a and b are both positive even integers which of the following must

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49320
If a and b are both positive even integers which of the following must  [#permalink]

Show Tags

New post 08 Jun 2018, 12:11
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

89% (00:32) correct 11% (00:42) wrong based on 76 sessions

HideShow timer Statistics

If \(a\) and \(b\) are both positive even integers, which of the following must be even?

I. \(a^b\)

II. \((a+1)^b\)

III. \(a^{(b+1)}\)


(A) I only
(B) II only
(C) I and II only
(D) I and III only
(E) I, II, and III

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Intern
Intern
User avatar
B
Joined: 01 Jan 2018
Posts: 44
CAT Tests
Re: If a and b are both positive even integers which of the following must  [#permalink]

Show Tags

New post 08 Jun 2018, 12:19
Even number to the power Even is always even. Hence I is true.

Odd number to the power Even is Odd. In fact odd number to the power Even/Odd is always odd. Hence II is False

Even number to the power Odd is Even. Hence III is True.

Option D.
e-GMAT Representative
User avatar
P
Joined: 04 Jan 2015
Posts: 2014
Re: If a and b are both positive even integers which of the following must  [#permalink]

Show Tags

New post 08 Jun 2018, 12:32

Solution



Given:
    • a and b are both positive even integers

To find:
    • Out of the given options, which of them are always even

Approach and Working:
In this case, we only know both a and b individually are even numbers

Now, considering the expressions one by one,
    • \(a^b = (even)^{even} = even\)
    • \((a + 1)^b = (odd)^{even} = odd\)
    • \(a^{(b+1)} = (even)^{odd} = even\)

Therefore, 1 and 3 will be always even.

Hence, the correct answer is option D.

Answer: D
_________________








Register for free sessions
Number Properties | Algebra |Quant Workshop

Success Stories
Guillermo's Success Story | Carrie's Success Story

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Must Read Articles
Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets



| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Director
Director
User avatar
P
Status: Learning stage
Joined: 01 Oct 2017
Posts: 859
WE: Supply Chain Management (Energy and Utilities)
Premium Member CAT Tests
Re: If a and b are both positive even integers which of the following must  [#permalink]

Show Tags

New post 08 Jun 2018, 18:59
Bunuel wrote:
If \(a\) and \(b\) are both positive even integers, which of the following must be even?

I. \(a^b\)

II. \((a+1)^b\)

III. \(a^{(b+1)}\)


(A) I only
(B) II only
(C) I and II only
(D) I and III only
(E) I, II, and III


Given a>0, b>0 & a,b are even.

Let's say a=2. b=4

I. \(a^b\)=\(2^4\)=16 which is even.

II. \((a+1)^b\)=\(3^4\)=81 which is not even.

III. \(a^{(b+1)}\)=\(2^5\)=32 which is even

Hence ans option D.
_________________

Regards,

PKN

Rise above the storm, you will find the sunshine

Director
Director
User avatar
G
Joined: 31 Oct 2013
Posts: 578
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
If a and b are both positive even integers which of the following must  [#permalink]

Show Tags

New post 10 Jun 2018, 14:50
Bunuel wrote:
If \(a\) and \(b\) are both positive even integers, which of the following must be even?

I. \(a^b\)

II. \((a+1)^b\)

III. \(a^{(b+1)}\)


(A) I only
(B) II only
(C) I and II only
(D) I and III only
(E) I, II, and III



It's a fundamental question based on rules of exponents. Why do we use exponent? it's a short cut multiplication.

here are some rules:
1.even integer having even power will always yield even. For example: 2*2*2*2*2*2*2*2............ultimate results will be even.
2. An odd integer having odd or even power will always yield odd integer. 3*3*3*3 = 81 which is an odd.
3. An even integer having odd or even power will always yield even integer. 2*2*2*2*2 = 32 even .

Thus D is the best answer.
Manager
Manager
avatar
G
Joined: 31 Jul 2017
Posts: 126
Location: Tajikistan
Concentration: Finance, Economics
Schools: Booth '21, CBS '21
GMAT 1: 690 Q48 V35
GRE 1: Q164 V162
GPA: 3.85
WE: Accounting (Investment Banking)
Premium Member CAT Tests
Re: If a and b are both positive even integers which of the following must  [#permalink]

Show Tags

New post 12 Jun 2018, 04:17
I go with D because
1. even^even is always even, try with numbers 2 and 4 (works)
2. odd^even is odd, try with 3^2 (doesnt work)
3. even^off is even, try with 2 and 3 (works).
Conditions 1 and 3 satisfy the question asked, hence answer would be D
GMAT Club Bot
Re: If a and b are both positive even integers which of the following must &nbs [#permalink] 12 Jun 2018, 04:17
Display posts from previous: Sort by

If a and b are both positive even integers which of the following must

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  

Events & Promotions

PREV
NEXT


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.